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Mathematics
Problem
Point
P
(
x
,
y
,
5
)
P(x,y,5)
P
(
x
,
y
,
5
)
lies on the plane
x
+
2
y
+
z
=
17
x+2y+z=17
x
+
2
y
+
z
=
17
and is
10
10
10
units from
Q
(
2
,
1
,
3
)
Q(2,1,3)
Q
(
2
,
1
,
3
)
. If
x
>
y
x>y
x
>
y
, determine
(
x
,
y
)
(x,y)
(
x
,
y
)
. a)
(
18
−
8
26
5
,
21
+
4
26
5
)
\left(\dfrac{18-8\sqrt{26}}{5},\,\dfrac{21+4\sqrt{26}}{5}\right)
(
5
18
−
8
26
,
5
21
+
4
26
)
b)
(
18
+
4
29
5
,
21
−
2
29
5
)
\left(\dfrac{18+4\sqrt{29}}{5},\,\dfrac{21-2\sqrt{29}}{5}\right)
(
5
18
+
4
29
,
5
21
−
2
29
)
c)
(
18
+
8
26
5
,
21
−
4
26
5
)
\left(\dfrac{18+8\sqrt{26}}{5},\,\dfrac{21-4\sqrt{26}}{5}\right)
(
5
18
+
8
26
,
5
21
−
4
26
)
d)
(
22
+
8
21
5
,
−
19
+
4
21
5
)
\left(\dfrac{22+8\sqrt{21}}{5},\,\dfrac{-19+4\sqrt{21}}{5}\right)
(
5
22
+
8
21
,
5
−
19
+
4
21
)
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